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DPDA Deterministic PDA

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Fact 1: Regular languages. Context-free languages. Prof. Busch ... Fact 2: (we can prove this using pumping lemma. for context-free languages) Prof. Busch - LSU ... – PowerPoint PPT presentation

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Title: DPDA Deterministic PDA


1
DPDADeterministic PDA

2
Deterministic PDA DPDA
Allowed transitions
(deterministic choices)
3
Allowed transitions
(deterministic choices)
4
Not allowed
(non deterministic choices)
5
DPDA example
6
Definition
A language is deterministic context-free if
there exists some DPDA that accepts it
Example
The language
is deterministic context-free
7
Example of Non-DPDA (PDA)
8
Not allowed in DPDAs
9
PDAs Have More Power thanDPDAs

10
It holds that
Deterministic Context-Free Languages (DPDA)
Context-Free Languages PDAs
Since every DPDA is also a PDA
11
We will actually show
Deterministic Context-Free Languages (DPDA)
Context-Free Languages (PDA)
12
The language is
We will show
  • is context-free
  • is not deterministic context-free

13
Language is context-free
14
Theorem
The language
is not deterministic context-free
(there is no DPDA that accepts )
15
Proof
Assume for contradiction that
is deterministic context free
Therefore
there is a DPDA that accepts
16
DPDA with
accepts
accepts
17
DPDA with
Such a path exists due to determinism
18
Fact 1
The language is not
context-free
(we will prove this at a later class
using pumping lemma for context-free languages)
19
Fact 2
The language is not
context-free
(we can prove this using pumping lemma for
context-free languages)
20
We will construct a PDA that accepts
which is a contradiction!
21
DPDA
Replace with
Modify
DPDA
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A PDA that accepts
Connect the final states of with the
final states of
23
Since is accepted by a
PDA
it is context-free
Contradiction!
(since is not
context-free)
24
Therefore
Is not deterministic context free
There is no DPDA that accepts it
End of Proof
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